Question

Simplify. cos^2[(pi/2) - x] + cos^2[(pi/2) - x] + cos^2x

Answer 1

Numerator
cos(π/2−x)=cos(π/2)cosx+sin(π/2)sinx

now cos(π/2)=0 and sin(π/2)=1

simplifies to : 0 + sinx = sinx

Denominator

sin(π/2−x)=sin(π/2)cosx+cos(π/2)sinx

simplifies to : cosx + 0 = cosx

⇒cos(π/2−x)sin(π/2−x)=sinx/cosx=tanx